Brandy Staples, right, knocked on doors in Bath, Me., last week on behalf of a referendum to expand Medicaid. She urged her second cousin Cynthia Mitchell, center, to vote for it.CreditCreditSarah Rice for The New York Times

PORTLAND, Me. — Night after night, in the sharp autumn air, canvassers are knocking on doors across Maine in hopes of getting tens of thousands of poor adults insured through Medicaid. Gov. Paul LePage, a Republican, has five times vetoed expanding access to the program under the Affordable Care Act. Next month, voters here will be the first in the nation to decide the issue by referendum.

But even in this liberal city, canvassers have encountered resistance from some as they stood on creaky porches and leaf-strewn steps to argue, as Lily SanGiovanni did the other night, that “health care is a human right.”

“My only question is where is the money coming from?” asked Michael Bunker, 35, a gym owner who spent 10 minutes debating the issue on his doorstep with Ms. SanGiovanni, a volunteer with Mainers for Health Care, the lead pro-expansion group. “I agree everyone should have free health care, it sounds great. But I can’t sign anything that’s just going to add to the federal debt.”

The referendum on Nov. 7 represents a new front in the pitched political battles over health care. Maine is one of 19 states whose Republican governors or legislatures have refused to expand Medicaid under Obamacare, and the other holdouts — particularly Utah and Idaho, where newly formed committees are working to get a Medicaid expansion question on next year’s ballot — are closely watching the initiative, whose outcome may offer clues about the salience of the issue in next year’s midterm congressional elections.

After President Trump and Republicans in Congress spent much of the year trying to repeal the health law and cut spending on Medicaid, a half-century-old entitlement program that covers one in five Americans, the pro-expansion side in Maine is hoping to benefit from energized public support for it.

Turnout may be the biggest challenge for the advocacy groups leading the effort. There are no national or statewide races here to drive people to the polls this year. And Mr. LePage’s stance on government safety net programs appeals to many voters in the state’s more rural regions. He derides Medicaid expansion as “pure welfare” that would burden the state’s taxpayers.

Senator Susan Collins of Maine, one of the few Republicans who firmly opposed the Obamacare repeal bills, is not taking a position on the ballot measure — she never does on referendums, according to her staff. But leaders of the campaign are hoping her outspoken support for Medicaid during the repeal battles will help.

About 80,000 additional Mainers would become eligible for the program if the ballot measure were to succeed, according to the nonpartisan Maine Office of Program and Fiscal Review, although those with income above the poverty line currently qualify for subsidized coverage through the Obamacare marketplace. In all, more than 2.5 million poor uninsured adults across the country would gain access to Medicaid if the holdout states expanded the program, joining about 11 million who have already signed up under the law.

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Brandy Staples, left, and Kate Brennan went door-to-door to urge voters to back Medicaid expansion in Bath, Me., last week.CreditSarah Rice for The New York Times

Kari Medeiros, 40, of Eastport, a tiny town in the state’s poorest county, earns less than $5,000 a year cleaning houses and pet sitting, and has back pain that has worsened to the point where she can barely mop and sweep.

“With MaineCare I believe I’d be able to find a provider who would see me,” she said, referring to the state’s Medicaid program. “But a lot of people here don’t vote. So many families here are having addiction problems with their loved ones, and they’re not focused on going to vote — even though those are the people that need it the most.”

Under the Affordable Care Act, the federal government picked up the entire cost of new enrollees under Medicaid expansion for the first three years and will continue to pay at least 90 percent. (States cover a significantly larger portion of the expenses of the regular Medicaid program.) The law allows any citizen with income up to 138 percent of the poverty level — $16,642 for an individual, $24,600 for a family of four — to qualify.

The main arguments for expanding the program here are that it would help financially fragile rural hospitals, create jobs and provide care for vulnerable people who have long gone without it.

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R.J. Miller, 33, who suffers from psoriatic arthritis that causes severe joint pain and swelling, said he worries about relying indefinitely on free care to control his condition.CreditSarah Rice for The New York Times

But Mr. LePage and other opponents say that Maine should know better. The state undertook a more modest expansion of Medicaid in 2002, under former Gov. Angus King, an independent. Afterward, Maine struggled with budget shortfalls and fell behind on Medicaid payments to hospitals.

“People don’t want to acknowledge the unintended consequences that Maine has already experienced,” said Brent Littlefield, a political adviser to Mr. LePage who is serving as the spokesman for Welfare to Work, the committee leading the opposition. He said that even with the federal government paying most of the cost — a situation that could change if Congress eventually succeeds in repealing Obamacare — the state could owe close to $100 million a year, according to estimates from the LePage administration.

The Office of Program and Fiscal Review has estimated a lower state cost, about $54 million a year once the federal share drops to 90 percent in 2021. Maine would not receive the full 90 percent match for parents of young children because many already qualify for the program.

Maine’s legislature, which is controlled by Democrats in the House and Republicans, by one vote, in the Senate, could move to block the referendum if it were to pass, but since it voted for Medicaid expansion five times already, supporters and opponents alike believe it is unlikely to meddle. And the governor would have no authority to veto the outcome. The only other threat would be if Congress succeeded in repealing the Affordable Care Act and ended the Medicaid expansion program.

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Robert Schmidt, a veteran, said he was conflicted about supporting free coverage for low-income people regardless of whether they worked.CreditSarah Rice for The New York Times

Supporters of the measure have knocked on 150,000 doors since July and have run four television ads statewide. Mainers for Health Care had raised about $480,000 as of early October, including $375,000 from the Fairness Project, a left-leaning group founded in California. It is putting out national appeals for donations, including through Organizing for Action, the political group that grew out of former President Barack Obama’s campaigns.

Welfare to Work had raised $192,500, with its contributions coming from a handful of frequent Republican donors in the state. Mr. Littlefield would not discuss the opposition’s strategies, but the group has at least two ads running on television statewide and Mr. LePage has been blasting the initiative on talk radio and in other public comments.

Canvassers for the measure have found one of the biggest obstacles is lack of knowledge about the issue, even among those who would benefit. Nicole Simard, 33, interrupted Ms. SanGiovanni a few seconds into her pitch, saying: “I agree, I agree. I have friends that are suffering right now, that don’t have insurance. My sister is one.” Like many people Ms. SanGiovanni encountered that night, Ms. Simard said that she had not been aware of the referendum but that she would vote for it.

“Absolutely, 100 percent,” she promised.

The following night in Bangor, about two hours north, canvassers encountered Robert Schmidt, a veteran who said he was conflicted about free coverage for low-income people regardless of whether they worked.

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Nurses Cokie Giles, far left, and Cynthia Martinez-Edgar, far right, talked to James Klemenz, second from left, and Kirsten Reed at their home while going door-to-door to urge voters to back Medicaid expansion.CreditSarah Rice for The New York Times

“I had to sign my life away to get my free care,” he said of the government coverage he receives as a veteran. “I can’t do handouts. On the other hand, with all the money we spend across the world, why aren’t we taking care of our own people?”

Mr. Schmidt, who is 53 and works at a big-box store, said he was not sure how he would vote.

A few houses down, his neighbors Kirsten Reed and James Klemenz told the canvassers that they would eagerly vote for Medicaid expansion now that they had been reminded about it. Mr. Klemenz, a carpenter who is uninsured, and Ms. Reed, an artist and writer who has insurance, said they had seen a pro-expansion ad on television but had forgotten about it.

“I could have easily been someone who believes in this but didn’t get out and vote,” Ms. Reed, 44, told the canvassers, Cokie Giles and Cynthia Martinez-Edgar, both nurses.

State Representative Heather Sirocki, a Republican active in fighting the ballot measure, said the uninsured could always sign up for charity care at hospitals, which are obligated to provide it to people under a certain income level.

At the Oasis Free Clinic in Brunswick, which sees about 450 uninsured patients a year, R. J. Miller, 33, who suffers from psoriatic arthritis that causes severe joint pain and swelling, said he worried about relying indefinitely on free care to control his condition.

“I’ve lived in other countries where nobody’s going to let you fall all the way down,” said Mr. Miller, a jazz drummer. “We buy into the American legend of, ‘You can take care of yourself anywhere, kid.’ That’s a bad lesson to teach everybody.”

Correction:

A previous version of this article misstated the governor who initiated an expansion of Medicaid in Maine in 2002. It was Angus King, an independent, not John Baldacci, a Democrat.

Correction:

An article on Saturday about a coming health care referendum in Maine misstated the surname of a man in Bangor, Me. He is James Klemenz, not James Smith. (A picture caption gave his correct name.) The article also described incorrectly the insurance status of Mr. Klemenz’s partner, Kirsten Reed. She is not uninsured.

A version of this article appears in print on , on Page A1 of the New York edition with the headline: Maine Governor Blocked Medicaid Expansion. Now It’s on Ballot.. Order Reprints | Today’s Paper | Subscribe